Construct the following angles and verify by measuring them by a protractor:

105°

Solution

105°
Given: A ray OA.
Required: To construct an angle of 105° at O.
Steps of Construction:
1. Taking O as centre and some radius, draw an arc of a circle, which intersects OA, say at a point B.

2. Taking B as centre and with the same radius as before, draw an are intersecting the previously drawn arc, say at a point C.
3. Taking C as centre and with the same radius as before, draw an arc intersecting the arc drawn in step 1, say at D.
4. Draw the ray OE passing through C. Then ∠EOA = 60°.
5. Draw the ray OF passing through D. Then ∠FOE = 60°.
6. Next, taking C and D as centres and with the radius more than $1 half$ CD, draw arcs to intersect each other, say at G.
7. Draw the ray OG intersecting the arc drawn in step 1 at H. This ray OG is the bisector of the angle FOE,
$straight i. straight e. space angle FOG equals angle EOG equals 1 half angle FOE equals 1 half left parenthesis 60 degree right parenthesis equals 30 degree Thus comma space angle GOA equals angle GOE plus angle EOA equals 30 degree plus 60 degree equals 90 degree$
8. Next, taking H and D as centres and with the radius more than $1 half$ HD, draw arcs to intersect each other, say at I. 9. Draw the ray OI. This ray OI is the bisector of the angle FOG,
$straight i. straight e. comma space space angle FOI equals angle GOI equals 1 half angle IOG equals 1 half left parenthesis 30 degree right parenthesis equals 15 degree$
Thus, ∠IOA = ∠IOG + ∠GOA = 15° + 90° = 105°. On measuring the ∠IOA by protractor, we find that ∠IOA = 105°.
Thus, the construction is verified.

For Daily Free Study Material Join wiredfaculty

Surface Areas And Volumes

Construct the following angles and verify by measuring them by a protractor:

105°

Some More Questions From Surface Areas and Volumes Chapter

Construct an equilateral triangle, given its side and justify the construction.

Construct an equilateral triangle with one side 6 cm.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location

For Daily Free Study Material Join wiredfaculty

Surface Areas And Volumes

Construct the following angles and verify by measuring them by a protractor:105°

Some More Questions From Surface Areas and Volumes Chapter

Construct an equilateral triangle, given its side and justify the construction.

Construct an equilateral triangle with one side 6 cm.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Construct the following angles and verify by measuring them by a protractor:

105°